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How to calculate the integral of a erf times another function?

  1. Oct 5, 2013 #1
    Hi

    I'm encountered the calculation of this function [itex]\int^{\infty}_0 e^{-x^2} f(x) dx[/itex]. How to do it? Thanks.
     
  2. jcsd
  3. Oct 5, 2013 #2

    SteamKing

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    Depends of what f(x) is.
     
  4. Oct 5, 2013 #3
    SteamKing, thanks. I have another problem, which I encountered in the same paper. Maybe you could help me. Thanks in advance.

    The author asserts that [itex]V(k,t)=V(k,0)e^{-k^2t}+ k\int^{t}_{0}C(t')e^{k^2(t'-t)}dt'[/itex] implies [itex]V(k,t)=C(t)/k + \mathcal{O}(k^{-3})[/itex] when t>0 and [itex]k\rightarrow \infty[/itex]. Could you see this?
     
  5. Oct 5, 2013 #4

    mathman

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    I haven't worked out the details.
    It looks like the V(k,0) term -> 0 very fast, so it can be ignored.
    The lntegrand of the integral looks as if -> δ(t'-t)/k2.
     
  6. Oct 5, 2013 #5
    Mathman, thanks. I agree with you, but I need the detail to understand it.. Since it seems it is impossible to expand the exponential term in the integral, I don't know other techniques to evaluate the integral...
     
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